Large language models (LLMs) are increasingly applied as automatic evaluators for natural language generation assessment often using pairwise comparative judgements. Existing approaches typically rely on single judges or aggregate multiple judges assuming equal reliability. In practice, LLM judges vary substantially in performance across tasks and evaluation aspects, and their judgment probabilities may be biased and inconsistent. Furthermore, human-labelled supervision for judge calibration may be unavailable. We first empirically demonstrate that inconsistencies in LLM comparison probabilities exist and show that it limits the effectiveness of direct probability-based ranking. To address this, we study the LLM-asa-jury setting and propose BT-sigma, a judge-aware extension of the Bradley-Terry model that introduces a discriminator parameter for each judge to jointly infer item rankings and judge reliability from pairwise comparisons alone. Experiments on benchmark NLG evaluation datasets show that BT-sigma consistently outperforms averaging-based aggregation methods, and that the learned discriminators strongly correlate with independent measures of the cycle consistency of LLM judgments. Further analysis reveals that BT-sigma can be interpreted as an unsupervised calibration mechanism that improves aggregation by modelling judge reliability.
Figures & tables
Figure 1: Hard/Soft Bradley-Terry and BT- σ in the LLM-as-a-jury setting. Hard BT uses binary comparisons ( p(i≻j)∈{0,1} ), while soft BT uses probabilistic preferences. BT- σ extends soft BT with judge-specific discriminators σk to model judge reliability.
Model
Method
COH
CON
FLU
REL
ALL
Llama-3.1-8B
Avg-Prob
43.87
31.89
26.32
42.39
36.12
hard BT
46.88
45.47
37.09
50.69
45.03
soft BT
48.40
45.12
36.80
51.02
45.33
Llama-3.2-3B
Avg-Prob
27.72
5.93
7.12
30.61
17.84
hard BT
13.31
0.28
17.24
33.15
16.00
soft BT
13.36
0.53
14.50
34.40
15.70
Table 1: Spearman correlations (SRC) of each individual LLM judge on SummEval. The best results for each aspect on each model are underlined.
Figure 2: Cycle inconsistency rate on different LLMs, evaluated on SummEval (COH).
Figure 3: SRC barchart for different aggregation methods on SummEval and Topical-Chat (ALL aspects).
SummEval
Topical-Chat
Method
COH
CON
FLU
REL
COH
CNT
ENG
NAT
Avg-Prob
52.55
41.75
36.21
50.09
56.01
49.39
61.62
51.53
hard BT
51.26
45.72
40.07
52.32
59.31
50.25
62.57
56.90
soft BT
53.94
47.86
42.69
53.11
60.05
53.87
61.87
58.20
Temp-BT
56.21
47.40
41.88
55.14
56.88
52.21
63.86
60.65
BT- σ
57.38
47.47
42.99
54.15
59.02
56.30
63.49
60.56
Table 2: Aggregation performance measured by Spearman correlations (SRC) between aggregated rankings and human judgments, evaluated on SummEval and Topical-Chat.
Figure 4: Scatter plot of 1/σk and LLM performance with Avg-Prob, measured by SRC, on SummEval (ALL).
Dataset
Metric
COH
CON
FLU
REL
ALL
SummEval
PCC
84.11
54.05
60.75
71.92
72.21
SRC
80.95
66.67
76.19
76.19
85.71
COH
CNT
ENG
NAT
ALL
Topical-Chat
PCC
58.68
73.01
59.79
70.09
67.41
SRC
40.48
73.81
61.90
76.19
59.52
Table 3: Correlation between learned discriminator 1/σk and LLM rankings (PCC/SRC, %) on SummEval and Topical-Chat.
Dataset
Metric
COH
CON
FLU
REL
ALL
SummEval
PCC
90.17
90.33
85.72
88.25
90.29
SRC
97.62
97.62
88.10
97.62
95.24
COH
CNT
ENG
NAT
ALL
Topical-Chat
PCC
90.17
89.99
90.41
81.61
93.09
SRC
85.71
92.86
92.86
83.33
90.48
Table 4: Correlation between learned discriminator 1/σk and 1−CycleRate (PCC/SRC, %) on SummEval and Topical-Chat.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: Cycle inconsistency rate on different LLMs, evaluated on SummEval.
Figure 6: Scatter plot of 1/σk and 1−CycleRate on SummEval.
LLM
Method
COH
CNT
ENG
NAT
ALL
Llama-3.1-8B
Avg-Prob
51.82
44.06
62.61
46.90
51.34
hard BT
49.65
41.87
61.92
51.70
51.29
soft BT
50.57
45.92
58.73
49.62
51.21
Llama-3.2-3B
Avg-Prob
31.83
10.92
26.28
14.82
20.96
hard BT
26.09
6.61
30.70
15.93
19.83
soft BT
22.90
3.48
26.55
15.14
17.02
Appendix
Table 5: SRC of each individual LLM judge on Topical-Chat. The best results for each aspect on each model are underlined.
Figure 7: Cycle inconsistency rate on different LLMs, evaluated on Topical-Chat.
Figure 8: Scatter plots of judge discriminators on Topical-Chat.
# Judges
Avg-Prob
hard BT
soft BT
BT- σ
hard BT- σ
8
54.64
57.26
58.50
59.92
60.15
7
49.81
52.99
53.99
55.13
52.76
6
53.24
56.63
58.49
59.46
56.82
5
53.46
57.20
56.66
59.51
55.77
4
55.27
58.85
58.53
59.09
63.27
3
55.64
58.56
58.96
58.90
63.47
Appendix
Table 6: Overall SRC on Topical-Chat for different jury sizes.
Table 15
Figure 9: Scatter plot of 1/σk and LLM performance with Avg-Prob, measured by SRC on NovelEval (Relevance).
Figure 10: Cycle inconsistency rate on different LLMs, evaluated on NovelEval (Relevance)
Large language model (LLM)-as-a-judge research uses language models to score, compare, and verify AI outputs as scalable alternatives to human evaluation.